Card 1 of 20
EasyStudy card 1
Prompt
For \(x^2+bx+c\), what must factor constants \(m,n\) satisfy?
Answer
\(m+n=b\) and \(mn=c\).
MathChapter 11: Quadratic Functions
Flashcards
Factoring Trinomials Flashcards
Twenty cards on sign reasoning, sum-product pairs, the AC method, and verification.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
If \(c>0\) and \(b>0\), what signs do \(m,n\) have?
Answer
Both are positive.
Card 3 of 20
EasyStudy card 3
Prompt
If \(c>0\) and \(b<0\), what signs do \(m,n\) have?
Answer
Both are negative.
Card 4 of 20
EasyStudy card 4
Prompt
If \(c<0\), what can you conclude about factor signs?
Answer
One is positive and one is negative.
Card 5 of 20
EasyStudy card 5
Prompt
What is the first check before factoring a trinomial?
Answer
Look for a nontrivial greatest common factor.
Card 6 of 20
EasyStudy card 6
Prompt
In the AC method, what product must the split pair have?
Answer
\(ac\), the leading coefficient times the constant.
Card 7 of 20
EasyStudy card 7
Prompt
What sum must the AC-method pair have?
Answer
The middle coefficient \(b\).
Card 8 of 20
MediumStudy card 8
Prompt
What happens after finding the AC pair?
Answer
Rewrite \(bx\) as two terms using that pair.
Card 9 of 20
MediumStudy card 9
Prompt
What comes after splitting the middle term?
Answer
Group the four terms and factor each pair.
Card 10 of 20
MediumStudy card 10
Prompt
What must appear in both groups before the final factoring step?
Answer
The same binomial factor.
Card 11 of 20
MediumStudy card 11
Prompt
Why might you factor out a negative GCF?
Answer
It can leave a positive leading term and simplify sign reasoning.
Card 12 of 20
MediumStudy card 12
Prompt
How do you verify a trinomial factorization?
Answer
Expand the factors and compare all three coefficients.
Card 13 of 20
MediumStudy card 13
Prompt
What if no integer pair meets both sum and product conditions?
Answer
The trinomial is not factorable over the integers.
Card 14 of 20
MediumStudy card 14
Prompt
Factor \(x^2+x-20\).
Answer
\((x+5)(x-4)\).
Card 15 of 20
MediumStudy card 15
Prompt
Which pair splits \(13x\) when \(ac=36\)?
Answer
\(9x+4x\), since \(9+4=13\) and \(9(4)=36\).
Card 16 of 20
MediumStudy card 16
Prompt
Why is using \(c\) instead of \(ac\) a trap?
Answer
It fails when the leading coefficient is not \(1\).
Card 17 of 20
HardStudy card 17
Prompt
Factor \(6x^2+13x+6\).
Answer
\((3x+2)(2x+3)\).
Card 18 of 20
HardStudy card 18
Prompt
Factor \(8x^2-14x-15\).
Answer
\((4x+3)(2x-5)\).
Card 19 of 20
HardStudy card 19
Prompt
What does 'factor completely' require?
Answer
Extract the GCF and continue until no supported factor pattern remains.
Card 20 of 20
HardStudy card 20
Prompt
What is the quickest check for a wrong AC split?
Answer
Its two coefficients must add to \(b\) and multiply to \(ac\).
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